Natural Computing

, Volume 10, Issue 1, pp 613–632 | Cite as

The computational power of membrane systems under tight uniformity conditions

  • Niall MurphyEmail author
  • Damien Woods


We apply techniques from complexity theory to a model of biological cellular membranes known as membrane systems or P-systems. Like Boolean circuits, membrane systems are defined as uniform families of computational devices. To date, polynomial time uniformity has been the accepted uniformity notion for membrane systems. Here, we introduce the idea of using AC 0-uniformity and investigate the computational power of membrane systems under these tighter conditions. It turns out that the computational power of some systems is lowered from P to NL when using AC 0-semi-uniformity, so we argue that this is a more reasonable uniformity notion for these systems as well as others. Interestingly, other P-semi-uniform systems that are known to be lower-bounded by P are shown to retain their P lower-bound under the new tighter semi-uniformity condition. Similarly, a number of membrane systems that are known to solve PSPACE-complete problems retain their computational power under tighter uniformity conditions.


Membrane systems P-systems Computational complexity NL Uniformity Semi-uniformity 



We would like to thank Mario J. Pérez-Jiménez and Agustín Riscos-Núñez and the other members of the Research Group on Natural Computing at the University of Seville for interesting discussions and for hosting Niall Murphy while later versions of this article were written. We would also like to thank Antonio E. Porreca for stimulating discussions about uniformity and the anonymous reviewers for their rigour in checking Sect. 5. Niall Murphy is supported by the Irish Research Council for Science, Engineering and Technology. Damien Woods is supported by Junta de Andalucía grant TIC-581 (Spain) and National Science Foundation Grant 0832824, the Molecular Programming Project (USA).


  1. Alhazov A, Pérez-Jiménez MJ (2007) Uniform solution to QSAT using polarizationless active membranes. In: Durand-Lose J, Margenstern M (eds) Machines, computations and universality (MCU). LNCS, vol 4664. Springer, Orléans, pp 122–133Google Scholar
  2. Allender E, Gore V (1993) On strong separations from AC0. DIMACS Ser Discret Math Theor Comput Sci 13:21–37MathSciNetGoogle Scholar
  3. Barrington DAM, Immerman N, Straubing H (1990) On uniformity within NC1. J Comput Syst Sci 41(3):274–306MathSciNetzbMATHCrossRefGoogle Scholar
  4. Greenlaw R, Hoover HJ, Ruzzo WL (1995) Limits to parallel computation: P-completeness theory. Oxford University Press, New YorkzbMATHGoogle Scholar
  5. Gutiérrez-Naranjo MA, Pérez-Jiménez MJ, Riscos-Núñez A, Romero-Campero FJ (2006) Computational efficiency of dissolution rules in membrane systems. Int J Comput Math 83(7):593–611MathSciNetzbMATHCrossRefGoogle Scholar
  6. Immerman N (1988) Nondeterministic space is closed under complementation. SIAM J Comput 17(5):935–938MathSciNetzbMATHCrossRefGoogle Scholar
  7. Immerman N (1989) Expressibility and parallel complexity. SIAM J Comput 18(3):625–638MathSciNetzbMATHCrossRefGoogle Scholar
  8. Murphy N (2010) Uniformity conditions for membrane systems: uncovering complexity below P. Ph.D. thesis, National University of Ireland, MaynoothGoogle Scholar
  9. Obtułowicz A (2001) Note on some recursive family of P systems with active membranes.
  10. Papadimitriou CH (1993) Computational complexitys. Addison Wesley, ReadingGoogle Scholar
  11. Păun G (2001) P systems with active membranes: attacking NP-complete problems. J Autom Lang Comb 6(1):75–90MathSciNetzbMATHGoogle Scholar
  12. Păun G (2002) Membrane computing. An introduction. Springer, BerlinzbMATHGoogle Scholar
  13. Păun G (2005) Further twenty six open problems in membrane computing. In: Proceedings of the third brainstorming week on membrane computing, Sevilla (Spain), January 31st–February 4th, pp 249–262Google Scholar
  14. Pérez-Jiménez MJ, Romero-Jiménez A, Sancho-Caparrini F (2003) Complexity classes in models of cellular computing with membranes. Nat Comput 2(3):265–285MathSciNetzbMATHCrossRefGoogle Scholar
  15. Sosík P, Rodríguez-Patón A (2007) Membrane computing and complexity theory: a characterization of PSPACE. J Comput Syst Sci 73(1):137–152zbMATHCrossRefGoogle Scholar
  16. Szelepcsényi R (1987) The method of forcing for nondeterministic automata. Bull EATCS 33:96–99zbMATHGoogle Scholar
  17. Zandron C, Ferretti C, Mauri G (2000) Solving NP-complete problems using P systems with active membranes. In: Antoniou I, Calude C, Dinneen M (eds) UMC ’00: proceedings of the second international conference on unconventional models of computation, London, UK, pp 289–301Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Computer ScienceNational University of Ireland MaynoothCo. KildareIreland
  2. 2.California Institute of TechnologyPasadenaUSA

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